A031932 Lower prime of a pair of consecutive primes having a difference of 14.

113, 293, 317, 773, 839, 863, 953, 1409, 1583, 1847, 2039, 2357, 2423, 2633, 2753, 2819, 2939, 3023, 3593, 3677, 3779, 3833, 3863, 4139, 4493, 4817, 4889, 4973, 5153, 5309, 5333, 5669, 5939, 6053, 6719, 7043, 7193, 7283, 7607, 7703

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n); i.e., a(n)^(1/n) is a strictly decreasing function of n (see comment lines of the sequence A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for primes, gaps between

Crossrefs

Subsequence of A124586.

Cf. A248855.

Programs

Magma

[p: p in PrimesUpTo(8000) | NextPrime(p)-p eq 14]; // Bruno Berselli, Apr 09 2013

Mathematica

Transpose[Select[Partition[Prime[Range[1000]],2,1],Last[#]-First[#] == 14&]] [[1]] (* Harvey P. Dale, Aug 24 2012 *)

PARI

is(n)=isprime(n) && nextprime(n+1)==n+14 \\ Charles R Greathouse IV, Sep 14 2015

Formula

a(n) = prime(A320705(n)). - R. J. Mathar, Apr 30 2024